3 Answers
3

One Soldier needs to be in every mission, so he is not allowed to be injured, or only very little.

What you could do is go for increased squad size early and make sure this particular soldier is always in your team and gets never injured. I cannot imagine doing this in ironman, but on easy and with loadable savegames this should be quite possible, since the achievement does not state any difficulty.

Also avoid the tutorial, since you can beat the first mission without losing anyone then.

I just finished my playthrough for this achievement, so here are my observations:

Easy difficulty is the way to go. Ironman should be disabled, just in case. This is going to take several hours, and there's no point in losing it at hour 9 because you left this box checked.

Disable the tutorial for sure, as this gives you a chance to bring home everybody from the first mission. I don't know if the first mission is counted, but I went ahead and picked one of the four from that mission anyhow.

Since avoiding injury is the name of the game, pick someone who will hang back. I used a sniper with squad sight - I'd almost recommend starting over from the beginning again if none of your initial four turn out to be sniper class.

I gave them a nickname like "Required" or "Achievement" so I knew right away if they were in the squad. If you've got the Elite Soldier Pack, you might also consider coloring them differently.

Psi training is pretty much out - it takes 10 days, and I've found it extremely rare that I go 10 days without a mission.

The early game was the trickiest part - at the beginning I actually had 3 soldiers who had been in every mission, just in case. However, once I had squadsight and a plasma sniper rifle there wasn't much left to do but win.

I played the game to delay the assault on the alien base until I had done almost all the research I possibly could. The enemies are pretty easy prior to the mind controlling aliens showing up, so this reduced my risk of injury or death. This took a bit of panic management with satellite coverage, but this is Easy difficulty, so it was nothing major.

Once I assaulted the base, I pretty much beelined the story missions and required buildings in order to get to the end as soon as possible.

I didn't have to skip any missions - my sniper never ended up in the medbay, and everything went fairly smoothly on the whole. The achievement popped for me when I was at the closing statistics screen.

Titan armor, or any other armor really adds leniency. For example titan armor adds 10 health to any soldier, so before even getting close to having to visit the sick bay they have to sustain 10 extra damage, thus if they take 9 damage only the armor is affected.

If you can play it safe and use ghost armor, the grappling hook really helps to move your soldiers around better and the ghost part makes sure that you don't alert any aliens while you're scouting, plus it gives a leniency of 6 health.

For those that are interested. I have achieved "Ain't no cavalry coming. I can confirm that if your specific soldier is injured, you can skip the next mission (S) until your soldier is able to go. Personally I skipped a council mission, My specific soldier (a support with ghost armor) was shot to the point where she needed to be revived on one mission I quickly revived her and healed her to full health. I still got the achievement. I just made sure she never got hurt again.